Skip to main content
SpringerLink
Log in

The theory of dispersion of chemically active solutes in a rectilinear flow field: The vector problem

  • Published:
Applied Scientific Research Aims and scope Submit manuscript

Abstract

In this paper and its sequel we seek an understanding of diffusion and reaction processes in multicomponent systems under convective conditions. To do this, we construct dispersion approximations to c, the solution of the vector convective diffusion equation, and to its transverse average, \(\bar c\). Dispersion coefficients are not the direct route to dispersion approximations in the vector problem. Yet constant long time dispersion coefficients exist and imply a rearrangement of the Hermite expansion of \(\bar c\). We deduce the rearrangement and introduce useful approximations thereto.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aris, R., On the dispersion of a solute in a fluid flowing through a tube, Proc. R. Soc. Lond. A 235 (1956) 67–77.

    Google Scholar 

  • Aris, R., Hierarchies of models in reactive systems, Dynamics and Modeling of Reactive Systems, ed. W.E. Stewart, W.H. Ray and C.C. Conley, Academic Press, New York, pp. 1–35.

  • DeGance, A.E. and L.E. Johns, The theory of dispersion of chemically active solutes in a rectilinear flow field, Appl. Sci. Res. 34 (1978) 189–225.

    Google Scholar 

  • DeGance, A.E. and L.E. Johns, The stability of vector renewal equations pertaining to heterogeneous chemical reaction systems, Quart. Appl. Math. 34 (1976) 69–83.

    Google Scholar 

  • DeGance, A.E. and L.E. Johns, On the equivalence of Hermite and power moments in the construction of dispersion approximations, Chem. Eng. Sci. 34 (1979) 1375–1376.

    Google Scholar 

  • Friedman, B., Principles and Techniques of Applied Mathematics, J. Wiley & Sons, London (1956).

    Google Scholar 

  • Gill, W.N. and R. Sankarasubramanian, Exact analysis of unsteady convective diffusion, Proc. R. Soc. Lond. A 316 (1970) 341–350.

    Google Scholar 

  • Halmos, P.R., Finite-Dimensional Vector Spaces, D. Van Nostrand Co., New York (1957).

    Google Scholar 

  • Johns, L.E. and A.E. DeGance, Dispersion approximations to the multicomponent convective diffusion equation for chemically active systems, Chem. Engng. Sci. 30 (1975) 1065–67.

    Google Scholar 

  • Naimark, M.A., Linear Differential Operators, Part I. Elementary Theory of Linear Differential Operators, Frederick Ungar Publishing, New York (1967).

    Google Scholar 

  • Sirovich, L., Techniques of Asymptotic Analysis, Springer-Verlag, New York (1971).

    Google Scholar 

  • Taylor, G.I., Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. Roy. Soc. Lond. A 219 (1953) 186–203.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Amoco Production Company, Research Center, P.O. Box 3385, 74102, Tulsa, OK, USA

    A. E. Degance

  2. Department of Chemical Engineering, University of Florida, 32611, Gainesville, FL, USA

    L. E. Johns

Authors
  1. A. E. Degance
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. E. Johns
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Degance, A.E., Johns, L.E. The theory of dispersion of chemically active solutes in a rectilinear flow field: The vector problem. Applied Scientific Research 42, 55–88 (1985). https://doi.org/10.1007/BF00382530

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00382530

Keywords

Search

Navigation